The Government of Pakistan prepared the second Perspective Plan in
198788 for the next fifteen years to set the long-term social and
economic policy framework. The Plan identified that the long-term
objectives could only be achieved if the education, skills, nutrition
and health of the people were improved. These objectives have recently
been operationalised in the donor supported Social Action Programme
(SAP). However, there is general recognition of the resource constraint
within which these objectives are to be achieved, especially given the
low priority that has been attached traditionally to allocations to the
social sectors. Therefore, the programme envisages the expansion of
primary infrastructure through an accelerated school construction
programme using cost-effective approaches to delivery including
need-based criteria for school location and changes in the pattern of
allocation of funds among sector inputs.

This paper examines cost-effectiveness of the primary education
sector in Pakistan and attempts to establish implications for a possible
future strategy. Section 2 presents the historical profile of the sector
from 1973 to 1991. Section 3 sets out the theoretical framework for
analysis. Sections 4 and 5 first estimate the costs and then identify
the determinants of spatial and inter-temporal variation in these costs.
Section 6 summarises the key conclusions.

2. TRENDS IN PRIMARY EDUCATION

Estimates of enrollment published by the Central Bureau of
Education of the Government of Pakistan indicate that it is increasing
at a faster pace than the growth in population of the relevant age
cohort (5-9 years) for each of the Provinces (see Table 1). In the
largest province, Punjab, primary enrollment has increased at more than
twice the growth rate in the relevant population cohort between 1973 and
1991. Starting from low base levels, female enrollments have shown an
even faster growth rate generally (except in Balochistan). The
differential in growth rates between enrollments and education inputs
(Teachers and Schools) indicates that the average number of students per
teacher has been increasing with the passage of time. Also the average
school size, measured as students per school, has been increasing.

The higher growth rate in the number of schools in the three more
relatively developed Provinces dearly shows the declining trend in the
number of teachers per school. This tends to imply that the quality of
education has been declining and that the share of capital costs in the
provision of education at the primary stage has been increasing over the
period.

3. THEORETICAL FRAMEWORK

Different approaches can be adopted for deriving the cost function
for primary education of provincial governments. One approach is to view
the provincial governments as engaging in a cost minimisation behaviour,
given knowledge of the production function of enrollments with respect
to inputs like schools, teachers, etc. in this view unit costs are the
minimum average costs for achieving a target enrollment ratio. However,
this approach assumes rational behaviour with full knowledge of the
production function, and no resource constraints such that targets can
be fully met. These assumptions are generally not satisfied in practice.

A more realistic view of how provincial governments behave is that
they generally operate in an overall resource constrained framework,
both for recurring and development expenditures, and that given the
overall quantum of resources available in the recurring budget and the
ADP, funds are allocated to primary education on the basis of
inter-sectoral priorities. According to this view then the actual choice
of level of inputs need not correspond to the cost minimising
combination. As such some inputs are likely to be overused while other
remain at sub-optimal levels. Fox example, if development allocations
for primary education are high, especially in recent years following the
launching of the SAP, then too many schools may be built relative to
teachers whose numbers may be constrained by lack of revenues to finance
recurring expenditures.

We set up the theoretical framework which is consistent with the
latter view. Accordingly the number of teachers, T, and the number of
schools, S is given exogenously by the size of current recurring and
development expenditure (past and present) allocations for primary
schools.

The total cost of primary education to provincial governments is
given by

where [w.sub.t] is the average wage rate (at constant prices) of
teachers. The wage rate includes overhead costs and cost of inputs
(books, etc.), [v.sub.t] is the rental price of capital and includes a
depreciation component and a component for the opportunity cost of
capital.

Information on public sector costs (both recurring and capital) of
providing education are contained in the annual budget documents of the
provincial governments. (1)

As the construction of schools is spread over a number of years,
the data on development outlay would need to be lagged differently for
each province. Because of data limitations a two-year lag for each of
the Provinces has been used.

The cost of providing primary education to a particular student is
the aggregate expenditure incurred over the five years he/she spends in
school. Further, as these costs are incurred at different periods of
time one needs to convert these into real terms.

The recurring expenditure series has been converted to real terms
(at constant prices of 1990-91) by inflating the nominal values by the
implicit deflator for the Public Administration and Defence sector of
the economy. The nominal development expenditures have been adjusted to
real terms using the implicit deflator for the Construction sector. The
trend growth rate in these implicit deflators indicates that the former
has been rising by 8.1 percent annually and the latter by 8.8 percent
annually. This would imply that the construction of more schools in
preference to the provision of more factor inputs may be less cost
efficient.

In real terms N.W.F.P. has been increasing its recurring
expenditure much more rapidly than the other Provinces. Sindh, however,
outstrips the others in its annual increase in development expenditure.
Inter-provincial differences in growth rates may be seen in Table 2.
These clearly highlight the priority in the mix of expenditure for each
of the provinces.

An important conclusion by comparison of the growth rates in Tables
1 and 2 respectively is the fast increase in expenditure relative to the
growth in physical inputs. This indicates that the unit cost, [C.sub.t],
of constructing a school has been rising in real terms while the real
recurring cost per teacher has also demonstrated some increase.

The output of the primary stage of education is the number of
students completing the fifth year. As information on completions,
successful or otherwise, is not available, the output at this stage has
been equated to the enrollment in class 5. The recurring costs spent on
a student produced by the system is the aggregate cost per enrollment
over the five year span.

The value of the base stock of schools in 1973 has been derived by
first estimating the average per school cost in real terms and then
applying this to the base quantum. This however, underestimates the
value of the base stock as it does not include the value of those
primary level class-rooms available in the higher category of schools
(middle and high). Information for this is not available. To this base
year estimate each year's addition to the capital stock is added.
This is then converted into an annualised stream by aggregating the
opportunity cost of the stock of schools each year and the current
year's depreciation. The Opportunity cost has been assumed to be
12.5 percent (the long-term return on government bonds) of the value of
the stock. The life-span of a primary shcool has been assumed to be 40
years. These have then been translated to the per student cost.

These province-wise estimates on a per student basis of primary
education are presented in Table 3. Table 4 summarises the growth rates
in enrollment and output costs.

It is also of some interest to note the inter-provincial variation
in costs. As of 1990-91, output cost at Rs 16,196 are the highest in
Balochistan, followed by Rs 15,985 in N.W.F.P., Rs 7,553 in Sindh and Rs
6,579 in the Punjab. Costs are relatively high in the former two
provinces becuase of the high component of capital costs due largely to
higher costs of constuction.

5. DETERMINANTS OF COSTS

The general specification of the average cost function (with
respect to enrollment) of primary education for provincial governments
is given by Equation (4). For econometric estimation we scale the number
of schools by the school going age population in age group of five to
nine years. The latter variable reflects potential demand. Similarly,
the number of teachers is scaled by the number of schools, to yield the
input mix. Also, since the impact on unit cost of [bar.S] and [bar.T] is
ambiguous, these variables enter in a polynomial form in the cost
function.

The resulting equation to be estimated is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ... ... (4)

where

[[bar.A].sub.t] = school going age population in year t ;

[Y.sub.t] = real per capita income;

[U.sub.t] = extent of urbanisation; and

[I.sub.t] = relative price index for wages to construction cost.

[Y.sub.t] is included to capture the real wage effect (inclusive of
labour into shcool construction) and a possible demand effect. [U.sub.t]
is a demand related variable. [I.sub.t] derives the cost implications of
a divergence between inflation in wages and construction costs.

The magnitudes of [[beta].sub.2] to [[beta].sub.6], are of special
significance. These will help in identifying the presence of economies
or diseconomies in the use of inputs.

Equation (4) is estimated on pooled time-series data for the four
provinces for the period, 1976-77 to 1990-91. The results are given in
Table 5. Intercept and slope dummies for the provinces have been used
wherever significant. The estimated equation demonstrates that there are
some significant inter-regional differences in these coefficients, with
Punjab and Sindh falling into one group and N.W.F.P. and Baloclaistan
into another group.

For all provinces the equation indicates that the average cost
falls initially and then rises subsequently with increase in
([[bar.S].sub.t]/[??]), the ratio of schools to school-going age
population. Therefore, there exists for each province an optimal
([bar.S]/[??]) which minimises unit costs. Any expansion in schools
beyond this level raises the unit cost. With regard to teachers per
school, we observe a rise in costs initially and then a fall with
increase in ([bar.T]/[bar.S]) up to a level beyond which costs rise once
again.

The estimated optimal cost minimising magnitudes of inputs for each
province are given in Table 6. The optimal number of schools per 1000
school-going age population in Punjab and Sindh is 6.76. The former
province was close to this level by 1990-91. For N.W.F.P. and
Balochistan the corresponding optimal magnitude is 3.54. N.W.F.P. is
already above this magnitude. Therefore, in at least two provinces of
the country, Punjab and N.W.F.P., the priority in allocation of
resources has to shift from school building. This activity can perhaps
only be justified on regional equity considerations in areas which are
backward and have low levels of coverage.

Table 6 also indicates there is underprovision generally of
teachers. It appears that their role in raising quality and demand for
primary education has not been fully recognised. Actual inputs of
teachers per school are below cost minimising levels in all provinces,
especially N.W.F.P. Overall we have the conclusion that the composition
of expenditure budgets (with the possible exception of Balochistan) has
to be dramatically altered. The recurring allocations for employing more
teachers need to be raised and simultaneously development allocations
scaled down. The same strategy is recommended for the Social Action
Programme. However, the expansion in the number of primary school
teachers raises issues of adequate training facilities, remuneration
levels and decentralisation of management down to community level to
increase accountability of teaching inputs.

6. CONCLUSIONS

This paper has examined the degree of cost effectiveness of the
primary education sector of Pakistan. Annual enrollment and output costs
have been estimated for each province for the period, 1976-77 to
1990-91. These have shown a rising trend generally because of the
increase in real recurring costs per teacher, in costs of school
contruction and because of the divergence in the physical level of use
of education inputs, schools and teachers, from the cost minimising
levels. In particular, the number of teachers is substantially below
optimal levels. This indicates that cost effectiveness of provision of
primary education can be significantly enhanced if the allocation of
funds is shifted towards recurring expenditures for employment of more
teachers away from development allocations for construction of new
schools.

Comments on "Cost Effectiveness in Primary Education: A Study
of Pakistan"

It is a pleasure to comment on the paper by Zafar H. Ismail, Hafiz
A. Pasha and A. Rauf Khan.

In the paper the authors considered the issues of cost
effectiveness of primary education and future strategy of resource
allocation. They noted that for improvement of human capital stock,
allocation of resources in the presence of resource constraint, has to
shift from construction of new schools to employment of more teachers. I
must acknowledge that it is an interesting and useful study. The issue
of economic efficiency in relation to resource allocation is a priority
area of the primary education element of the Social Action Programme
which was launched by the Government in 1992-93. The conclusion drawn
points to the right direction for planners and policy-makers. However,
there are some problems in respect to data, methodology and
specification of the cost function used in the study.

Under Section (2) "Trends in Primary Education", it is
stated that over the period 1972-91 the student/teacher ratio is
falling. However, based on the data provided in the Tables 1 and 2
inferences contrary to this can be drawn.

In designing the theoretical framework, it would be much more
useful if a province-specific framework be designed. A typical school,
location-specific to urban, semi-urban and rural is a case in point.
Instead of historical cost data, cost reflecting both fixed as well as
variable ones be estimated and then discounted to arrive at unit cost
may be prescribed as the standard one for the allocation of resources.
Needless to say that in view of the changing structure of inputs and
associated prices, the standard unit cost would need revision in due
course of time.

With reference to data, my two concerns are in regard to relevance
of primary school data and selection and application of deflators. On
the cost side, public expenditure data are used, whereas data on
enrollment, number of schools and teachers seem to relate to both public
and private sectors. Further in estimating the average capital cost of
schools, it appears that cost is overestimated as shelterless schools
constituting about 28 percent of total schools have not been taken care
of. As for the selection of deflators, the authors have used the
deflators of public administration and defence and construction sectors
respectively for deflating the recurrent and the development
expenditures. These may not be quite relevant. As the composition of
inputs of both the deflators are quite different and heavily biased
towards inputs with low weights for wage components and construction
inputs of schools. It may be appropriate that specific deflators of
public expenditure for the education sector are calculated and used. As
the time frame is the same and growth rates of both the implicit
deflators are dose, it may be useful, if methodology based on current
prices, which is also valid, may be used.

At the end I must add that the study is useful as it highlights the
current policy issues and serves well to contribute to our understanding
of the resource allocation process in the primary education sector.

Zafar H. Ismail and Hafiz A. Pasha are, respectively, Research
Fellow and Research Professor/Director at the Applied Economics Research
Centre, University of Karachi, Karachi, A. Rauf Khan is a Research
Officer at the Resource Mobilisation and Tax Reforms Commission.